SIAM
Journal on Scientific Computing

Volume 24, Number 6

pp. 1919-1929

## Numerical Computations of Viscous, Incompressible Flow Problems Using a
Two-Level Finite Element Method

### Faisal Fairag

**Abstract.** We consider two-level finite element discretization methods
for the stream function formulation of the Navier--Stokes equations. The
two-level method consists of solving a small nonlinear system on the coarse
mesh and then solving a linear system on the fine mesh. The basic result states
that the errors between the coarse and fine meshes are related superlinearly.
This paper demonstrates that the two-level method can be implemented to
approximate efficiently solutions to the Navier--Stokes equations. Two fluid
flow calculations are considered to test problems which have a known solution
and the driven cavity problem. Stream function contours are displayed showing
the main features of the flow.

**Key words.** two-level
method, Navier--Stokes equations, finite element, stream function formulation,
Reynolds number

**AMS Subject Classifications**. 65N35, 76M30,
76D05

**DOI**. 10.1137/S1064827500370895